I didn't say to not play the initial "get your attention" alarm. I was only referring to the silliness of a follow up alarm once your attention is already there.
I suppose a corner case would be another aircraft popping up ALSO squawking 7600 inside that "silence ring" calculated around the first one, but that's likely to be close enough that the snitch alarm would cover that one. Or the software could simply count. One aircraft silenced, inside this ring, second shows up, play the alarm again.
With proper analysis of the problem, there's no need to re-alarm on already known things every time the radar antenna goes roundy-round.